Probabilistic model for random uncertainties in steady state rolling contact

Abstract

Wear phenomena involve a large number of physical and mechanical parameters which are not always well known or controlled during relative movement between two bodies. Numerous industrial applications necessitate an evaluation of technological component life time and wear modelling often fails to give accurate estimation.We use the classical Archard's wear model where wear is related to dissipated power. It appears that great dispersion can occur in the estimation of dissipated power related to a lack of knowledge of certain parameters.We present here a probabilistic approach of the contact problem resolution. We consider the specific contact problem in the case of steady state rolling. A wear apparatus has been used to test different materials and we use the simplified model Fastsim to evaluate slip and tangential traction in the contact zone. For each parameter of the simulation, we construct a probabilistic density function with the only information available.A Monte-Carlo method is implemented and the resolution of numerous cases allows the dissipated energy to be evaluated as a mean value and a confidence region for 95% viability.

Uncertainty Quantification

“…− for robust analysis and uncertainty quantification of wave propagation in soil, urban cities, and biological tissues, [41,42,43,53,121,127]. − for robust analysis in computational structural dynamics with applications in engineering mechanics and space engineering, [16,17,20,48,124,161,168,169]. …”

“…48) in which the random matrix [G 0,A ] belongs to ensemble SG + 0 , with dimension μ (for a fixed substructure) or μ − μ rig (for a free substructure), and where ε > 0.The level of uncertainties for random matrix [A] is controlled by the coefficient of variation δ A of the random matrix [G 0,A ]. The generator of realizations of random matrix [G 0,A ] is detailed in Section 5.4.7.1.…”

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

“…[23,24,25,26,27] for theory and applications), it is possible to construct a pdf by searching the maximum of S ( f X ) under the constraint of the available information. Physical principles are not violated, since the resulting pdf maximizes the uncertainty while being compatible with the known information.…”

Contributions à la modélisation simplifiée de la mécanique des contacts roulants

“…Résumé : La modélisation de l'usure superficielle nécessite la mise en place d'un outil numérique de calcul des puissances dissipées lors du roulement sous charge de galets sur des pistes de came [1]. Compte tenu des dispersions relatives aux défauts géométriques et aux paramètres mal connus comme le coefficient de frottement par exemple, l'étude s'oriente vers une approche probabiliste [2] où le nombre de cas simulés devient très grand (environ 1000 simulations pour une géométrie et un chargement) et hors d'atteinte en des temps de calcul CPU raisonnables par une approche exacte. L'utilisation d'une approche simplifiée est alors nécessaire pour le calcul de la puissance dissipée dans le cas non hertzien généré par l'usure.…”

“…Abstract: Numerical simulation of superficial wear requires the implementation of computational tools for calculation of dissipated power during loaded contacts of roller on track cam [1]. Uncertainties due to geometrical defects or to not well known parameters such as the friction ratio for example, yields to a probabilistic approach [2] of the contact problem. Number of simulated cases becomes very important (approximately 1000 cases for a single geometry and loading) and cannot reasonably be treated by the exact approach which leads to long CPU time.…”